Andre was in the middle of a packed goalmouth when he poked the ball home 10 minutes into the second half.
His younger brother and fellow Ghana forward Jordan added the second goal three minutes from time as Marseille moved up to second place with 22 points, trailing PSG on goal difference.
"It is never easy to come and win here. We did not play a good first half but after the break we were rewarded for our efforts," winger Mathieu Valbuena told TV channel BeIN Sport.
"The most important thing is that we closed the gap on Paris. It's a good morale boost."
Marseille also have a game in hand on PSG who lost 2-1 at home to Saint-Etienne on Saturday.
Olympique Lyon are one point behind in third place after they beat Bastia 5-2 in a game where two players were sent off.
Toulouse are fourth on 19 points after they slumped to a 1-0 defeat at Girondins Bordeaux who moved up to seventh spot on 18.
Yoan Gouffran scored the goal from close range after collecting a splendid through ball from Jaroslav Plasil in the 87th minute.
Lyon were 2-0 up after 26 minutes thanks to Maxime Gonalons and Alexandre Lacazette but Wahbi Khazri pulled one back for Bastia.
Defender Dejan Lovren picked up a straight red card for fouling Bastia's Florian Thauvin and Jerome Rothen converted the resulting 32nd-minute penalty.
Fethi Harek then received a second yellow card in the 55th minute for bringing Lacazette down in the box and Lisandro Lopez converted from the spot for Lyon.
Late goals by Jimmy Briand and Steed Malbranque (penalty) rubbed salt into Corsican wounds.
Marseille, who lost their previous three games in all competitions without scoring a goal, struggled in the first half before their physical power started to make the difference.
Valbuena, one of Marseille's best players this season, played a key part in the victory.
For the first goal the France winger crossed the ball to Morgan Amalfitano whose shot was parried by Guillermo Ochoa into the path of Charles Kabore and his header was poked in by Andre Ayew.
Valbuena then set up Jordan Ayew who shook off his marker to coolly slot the ball past Ochoa with three minutes to go.
Winger Valbuena almost made it 3-0 in the closing stages but Mexico keeper Ochoa tipped his effort over the bar.
